Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".

Statement-1 :
r is equivalent to either q or p.

Statement-2 :
r is equivalent to ~(p ↔ ~q).

Question

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".

Statement-1 :
r is equivalent to either q or p.

Statement-2 :
r is equivalent to ~(p ↔ ~q).

ronit bhatiya · Answer

p : x is an irrational number
q : y is a transcendental number
r : x is a rational number iff y is a transcendental number
=> r : ~ p ↔ q
s₁ : q or p
s₂ : ~ (p↔~q)

p	q	~p	~q	r:~p↔q	s₁:q or p	p↔~q	s₂:~(p↔~q)
T	T	F	F	F	T	F	T
T	F	F	T	T	T	T	F
F	T	T	F	T	T	T	F
F	F	T	T	F	F	F	T

Based upon above chart
s₁ and r are not equivalent
s₂ and r are not equivalent

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Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number". Statement-1 : r is equivalent to either q or p. Statement-2 : r is equivalent to ~(p ↔ ~q).

Let p be the statement "x is an irrational number", q be the statement "y is a transcendental number", and r be the statement "x is a rational number if y is a transcendental number".

Statement-1 :
r is equivalent to either q or p.

Statement-2 :
r is equivalent to ~(p ↔ ~q).

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